Construction of differential operators having Bochner-Krall orthogonal polynomials as eigenfunctions

Abstract

Suppose {Q(n)}(n=0)(infinity) is a sequence of polynomials orthogonal with respect to the moment functional T = sigma + nu, where sigma is a classical moment functional (Jacobi, Laguerre, Hermite) and nu is a point mass distribution with finite support. In this paper, we develop a new method for constructing a differential equation having {Qn}(n=0)(infinity) as eigenfunctions. (c) 2005 Elsevier Inc. All rights reserved.